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<div class="title">FullPivLU.h</div>  </div>
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<div class="contents">
<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// Copyright (C) 2006-2009 Benoit Jacob &lt;jacob.benoit.1@gmail.com&gt;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160; </div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="preprocessor">#ifndef EIGEN_LU_H</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="preprocessor">#define EIGEN_LU_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160; </div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="preprocessor">#include &quot;./InternalHeaderCheck.h&quot;</span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160; </div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> {</div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160; </div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType_&gt; <span class="keyword">struct </span>traits&lt;FullPivLU&lt;MatrixType_&gt; &gt;</div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160; : traits&lt;MatrixType_&gt;</div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;{</div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;  <span class="keyword">typedef</span> MatrixXpr XprKind;</div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;  <span class="keyword">typedef</span> SolverStorage StorageKind;</div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;  <span class="keyword">typedef</span> <span class="keywordtype">int</span> StorageIndex;</div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;  <span class="keyword">enum</span> { Flags = 0 };</div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;};</div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160; </div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;} <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160; </div>
<div class="line"><a name="l00062"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html">   62</a></span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType_&gt; <span class="keyword">class </span><a class="code" href="classEigen_1_1FullPivLU.html">FullPivLU</a></div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;  : <span class="keyword">public</span> <a class="code" href="classEigen_1_1SolverBase.html">SolverBase</a>&lt;FullPivLU&lt;MatrixType_&gt; &gt;</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;{</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;    <span class="keyword">typedef</span> MatrixType_ MatrixType;</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;    <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1SolverBase.html">SolverBase&lt;FullPivLU&gt;</a> <a class="code" href="classEigen_1_1SolverBase.html">Base</a>;</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;    <span class="keyword">friend</span> <span class="keyword">class </span><a class="code" href="classEigen_1_1SolverBase.html">SolverBase</a>&lt;<a class="code" href="classEigen_1_1FullPivLU.html">FullPivLU</a>&gt;;</div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160; </div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;    EIGEN_GENERIC_PUBLIC_INTERFACE(<a class="code" href="classEigen_1_1FullPivLU.html">FullPivLU</a>)</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;    <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;      MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,</div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;    };</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::plain_row_type&lt;MatrixType, StorageIndex&gt;::type IntRowVectorType;</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::plain_col_type&lt;MatrixType, StorageIndex&gt;::type IntColVectorType;</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;    <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1PermutationMatrix.html">PermutationMatrix&lt;ColsAtCompileTime, MaxColsAtCompileTime&gt;</a> <a class="code" href="classEigen_1_1PermutationMatrix.html">PermutationQType</a>;</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;    <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1PermutationMatrix.html">PermutationMatrix&lt;RowsAtCompileTime, MaxRowsAtCompileTime&gt;</a> <a class="code" href="classEigen_1_1PermutationMatrix.html">PermutationPType</a>;</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::PlainObject PlainObject;</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160; </div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;    <a class="code" href="classEigen_1_1FullPivLU.html#af225528d1c6e623a2b1dce091907d13e">FullPivLU</a>();</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160; </div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;    <a class="code" href="classEigen_1_1FullPivLU.html#af225528d1c6e623a2b1dce091907d13e">FullPivLU</a>(<a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> rows, <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> cols);</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160; </div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> InputType&gt;</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;    <span class="keyword">explicit</span> <a class="code" href="classEigen_1_1FullPivLU.html#af225528d1c6e623a2b1dce091907d13e">FullPivLU</a>(<span class="keyword">const</span> <a class="code" href="structEigen_1_1EigenBase.html">EigenBase&lt;InputType&gt;</a>&amp; matrix);</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160; </div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> InputType&gt;</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;    <span class="keyword">explicit</span> <a class="code" href="classEigen_1_1FullPivLU.html#af225528d1c6e623a2b1dce091907d13e">FullPivLU</a>(<a class="code" href="structEigen_1_1EigenBase.html">EigenBase&lt;InputType&gt;</a>&amp; matrix);</div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160; </div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> InputType&gt;</div>
<div class="line"><a name="l00122"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a396f63d737e0613f41004e30be8fe3cf">  122</a></span>&#160;    <a class="code" href="classEigen_1_1FullPivLU.html">FullPivLU</a>&amp; <a class="code" href="classEigen_1_1FullPivLU.html#a396f63d737e0613f41004e30be8fe3cf">compute</a>(<span class="keyword">const</span> <a class="code" href="structEigen_1_1EigenBase.html">EigenBase&lt;InputType&gt;</a>&amp; matrix) {</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;      m_lu = matrix.<a class="code" href="structEigen_1_1EigenBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">derived</a>();</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;      computeInPlace();</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;      <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;    }</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160; </div>
<div class="line"><a name="l00134"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a3e7d7a53f5b7c4ba99013fe171ac5654">  134</a></span>&#160;    <span class="keyword">inline</span> <span class="keyword">const</span> MatrixType&amp; <a class="code" href="classEigen_1_1FullPivLU.html#a3e7d7a53f5b7c4ba99013fe171ac5654">matrixLU</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;LU is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;      <span class="keywordflow">return</span> m_lu;</div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;    }</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160; </div>
<div class="line"><a name="l00147"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#aad90c46ea08618ae485fce4e5f4677d0">  147</a></span>&#160;    <span class="keyword">inline</span> <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> <a class="code" href="classEigen_1_1FullPivLU.html#aad90c46ea08618ae485fce4e5f4677d0">nonzeroPivots</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;LU is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;      <span class="keywordflow">return</span> m_nonzero_pivots;</div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;    }</div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160; </div>
<div class="line"><a name="l00156"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a05cedf8dca6394355ef64c1ea1374b4a">  156</a></span>&#160;    RealScalar <a class="code" href="classEigen_1_1FullPivLU.html#a05cedf8dca6394355ef64c1ea1374b4a">maxPivot</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_maxpivot; }</div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160; </div>
<div class="line"><a name="l00162"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a3eb3aa0c37e06ffaf0c07b1eeb0995cc">  162</a></span>&#160;    EIGEN_DEVICE_FUNC <span class="keyword">inline</span> <span class="keyword">const</span> <a class="code" href="classEigen_1_1PermutationMatrix.html">PermutationPType</a>&amp; <a class="code" href="classEigen_1_1FullPivLU.html#a3eb3aa0c37e06ffaf0c07b1eeb0995cc">permutationP</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;LU is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;      <span class="keywordflow">return</span> m_p;</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;    }</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160; </div>
<div class="line"><a name="l00172"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a25b70ffbc88d804981c8874da55e7419">  172</a></span>&#160;    <span class="keyword">inline</span> <span class="keyword">const</span> <a class="code" href="classEigen_1_1PermutationMatrix.html">PermutationQType</a>&amp; <a class="code" href="classEigen_1_1FullPivLU.html#a25b70ffbc88d804981c8874da55e7419">permutationQ</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;LU is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;      <span class="keywordflow">return</span> m_q;</div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;    }</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160; </div>
<div class="line"><a name="l00192"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#adfc1e27ff60287be5313b5efc3559308">  192</a></span>&#160;    <span class="keyword">inline</span> <span class="keyword">const</span> internal::kernel_retval&lt;FullPivLU&gt; <a class="code" href="classEigen_1_1FullPivLU.html#adfc1e27ff60287be5313b5efc3559308">kernel</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;LU is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;      <span class="keywordflow">return</span> internal::kernel_retval&lt;FullPivLU&gt;(*<span class="keyword">this</span>);</div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;    }</div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160; </div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;    <span class="keyword">inline</span> <span class="keyword">const</span> internal::image_retval&lt;FullPivLU&gt;</div>
<div class="line"><a name="l00218"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#aa8cbf984141608e89b503125690d24d4">  218</a></span>&#160;      <a class="code" href="classEigen_1_1FullPivLU.html#aa8cbf984141608e89b503125690d24d4">image</a>(<span class="keyword">const</span> MatrixType&amp; originalMatrix)<span class="keyword"> const</span></div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;LU is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;      <span class="keywordflow">return</span> internal::image_retval&lt;FullPivLU&gt;(*<span class="keyword">this</span>, originalMatrix);</div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;    }</div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160; </div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;<span class="preprocessor">    #ifdef EIGEN_PARSED_BY_DOXYGEN</span></div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> Rhs&gt;</div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;    <span class="keyword">inline</span> <span class="keyword">const</span> <a class="code" href="classEigen_1_1Solve.html">Solve&lt;FullPivLU, Rhs&gt;</a></div>
<div class="line"><a name="l00246"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a614d3aa28e6af7b2af8630d3e2d022d8">  246</a></span>&#160;    <a class="code" href="classEigen_1_1FullPivLU.html#a614d3aa28e6af7b2af8630d3e2d022d8">solve</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1MatrixBase.html">MatrixBase&lt;Rhs&gt;</a>&amp; b) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;<span class="preprocessor">    #endif</span></div>
<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160; </div>
<div class="line"><a name="l00252"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#ae39fcfa8d1319472a5b2adfa7a28d9cf">  252</a></span>&#160;    <span class="keyword">inline</span> RealScalar <a class="code" href="classEigen_1_1FullPivLU.html#ae39fcfa8d1319472a5b2adfa7a28d9cf">rcond</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;PartialPivLU is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;      <span class="keywordflow">return</span> internal::rcond_estimate_helper(m_l1_norm, *<span class="keyword">this</span>);</div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;    }</div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160; </div>
<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;    <span class="keyword">typename</span> internal::traits&lt;MatrixType&gt;::Scalar <a class="code" href="classEigen_1_1FullPivLU.html#a71654e5c60a26407ecccfaa5b34bb0aa">determinant</a>() <span class="keyword">const</span>;</div>
<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160; </div>
<div class="line"><a name="l00292"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#abad257b6db0856d8ec52c6072f58f75d">  292</a></span>&#160;    <a class="code" href="classEigen_1_1FullPivLU.html">FullPivLU</a>&amp; <a class="code" href="classEigen_1_1FullPivLU.html#abad257b6db0856d8ec52c6072f58f75d">setThreshold</a>(<span class="keyword">const</span> RealScalar&amp; <a class="code" href="classEigen_1_1FullPivLU.html#ae2298a7a89749dee7d86f02ccacce0cb">threshold</a>)</div>
<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;    {</div>
<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;      m_usePrescribedThreshold = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;      m_prescribedThreshold = <a class="code" href="classEigen_1_1FullPivLU.html#ae2298a7a89749dee7d86f02ccacce0cb">threshold</a>;</div>
<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;      <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;    }</div>
<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160; </div>
<div class="line"><a name="l00307"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#aeafbb0b885cc4c28b53e77988ac5cfe3">  307</a></span>&#160;    <a class="code" href="classEigen_1_1FullPivLU.html">FullPivLU</a>&amp; <a class="code" href="classEigen_1_1FullPivLU.html#aeafbb0b885cc4c28b53e77988ac5cfe3">setThreshold</a>(Default_t)</div>
<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;    {</div>
<div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;      m_usePrescribedThreshold = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;      <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;    }</div>
<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160; </div>
<div class="line"><a name="l00317"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#ae2298a7a89749dee7d86f02ccacce0cb">  317</a></span>&#160;    RealScalar <a class="code" href="classEigen_1_1FullPivLU.html#ae2298a7a89749dee7d86f02ccacce0cb">threshold</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;      eigen_assert(m_isInitialized || m_usePrescribedThreshold);</div>
<div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;      <span class="keywordflow">return</span> m_usePrescribedThreshold ? m_prescribedThreshold</div>
<div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;      <span class="comment">// this formula comes from experimenting (see &quot;LU precision tuning&quot; thread on the list)</span></div>
<div class="line"><a name="l00322"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a25da97d31acab0ee5d9d13bdbb0569da">  322</a></span>&#160;      <span class="comment">// and turns out to be identical to Higham&#39;s formula used already in LDLt.</span></div>
<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;          : <a class="code" href="structEigen_1_1NumTraits.html">NumTraits&lt;Scalar&gt;::epsilon</a>() * RealScalar(m_lu.diagonalSize());</div>
<div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;    }</div>
<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160; </div>
<div class="line"><a name="l00332"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a8d31c78a17a70d56ef2d105d6b5efec3">  332</a></span>&#160;    <span class="keyword">inline</span> <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> <a class="code" href="classEigen_1_1FullPivLU.html#a8d31c78a17a70d56ef2d105d6b5efec3">rank</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160;      <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;LU is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;      RealScalar premultiplied_threshold = <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(m_maxpivot) * <a class="code" href="classEigen_1_1FullPivLU.html#ae2298a7a89749dee7d86f02ccacce0cb">threshold</a>();</div>
<div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;      <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> result = 0;</div>
<div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;      <span class="keywordflow">for</span>(<a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> i = 0; i &lt; m_nonzero_pivots; ++i)</div>
<div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160;        result += (<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(m_lu.coeff(i,i)) &gt; premultiplied_threshold);</div>
<div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;      <span class="keywordflow">return</span> result;</div>
<div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;    }</div>
<div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160; </div>
<div class="line"><a name="l00349"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a358cec49914ec3cd3707e6b79ae32d0b">  349</a></span>&#160;    <span class="keyword">inline</span> <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> <a class="code" href="classEigen_1_1FullPivLU.html#a358cec49914ec3cd3707e6b79ae32d0b">dimensionOfKernel</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;LU is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00352"></a><span class="lineno">  352</span>&#160;      <span class="keywordflow">return</span> cols() - <a class="code" href="classEigen_1_1FullPivLU.html#a8d31c78a17a70d56ef2d105d6b5efec3">rank</a>();</div>
<div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;    }</div>
<div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160; </div>
<div class="line"><a name="l00362"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a90dd33c632ba890175f61eac054bde98">  362</a></span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="classEigen_1_1FullPivLU.html#a90dd33c632ba890175f61eac054bde98">isInjective</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;LU is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;      <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1FullPivLU.html#a8d31c78a17a70d56ef2d105d6b5efec3">rank</a>() == cols();</div>
<div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;    }</div>
<div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160; </div>
<div class="line"><a name="l00375"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#af42b9cb6356658b92b2d1006aee73fc4">  375</a></span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="classEigen_1_1FullPivLU.html#af42b9cb6356658b92b2d1006aee73fc4">isSurjective</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;LU is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160;      <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1FullPivLU.html#a8d31c78a17a70d56ef2d105d6b5efec3">rank</a>() == rows();</div>
<div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;    }</div>
<div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160; </div>
<div class="line"><a name="l00387"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a0ee7753645eb31bcbd5faa459168b294">  387</a></span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="classEigen_1_1FullPivLU.html#a0ee7753645eb31bcbd5faa459168b294">isInvertible</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00389"></a><span class="lineno">  389</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;LU is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00390"></a><span class="lineno">  390</span>&#160;      <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1FullPivLU.html#a90dd33c632ba890175f61eac054bde98">isInjective</a>() &amp;&amp; (m_lu.rows() == m_lu.cols());</div>
<div class="line"><a name="l00391"></a><span class="lineno">  391</span>&#160;    }</div>
<div class="line"><a name="l00392"></a><span class="lineno">  392</span>&#160; </div>
<div class="line"><a name="l00400"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a34afc848d7fb22c7a56a053d3807d2cd">  400</a></span>&#160;    <span class="keyword">inline</span> <span class="keyword">const</span> <a class="code" href="classEigen_1_1Inverse.html">Inverse&lt;FullPivLU&gt;</a> <a class="code" href="classEigen_1_1FullPivLU.html#a34afc848d7fb22c7a56a053d3807d2cd">inverse</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00401"></a><span class="lineno">  401</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00402"></a><span class="lineno">  402</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;LU is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00403"></a><span class="lineno">  403</span>&#160;      eigen_assert(m_lu.rows() == m_lu.cols() &amp;&amp; <span class="stringliteral">&quot;You can&#39;t take the inverse of a non-square matrix!&quot;</span>);</div>
<div class="line"><a name="l00404"></a><span class="lineno">  404</span>&#160;      <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1Inverse.html">Inverse&lt;FullPivLU&gt;</a>(*<span class="keyword">this</span>);</div>
<div class="line"><a name="l00405"></a><span class="lineno">  405</span>&#160;    }</div>
<div class="line"><a name="l00406"></a><span class="lineno">  406</span>&#160; </div>
<div class="line"><a name="l00407"></a><span class="lineno">  407</span>&#160;    MatrixType <a class="code" href="classEigen_1_1FullPivLU.html#a191a4f598b0c192a83ab48984e87ee51">reconstructedMatrix</a>() <span class="keyword">const</span>;</div>
<div class="line"><a name="l00408"></a><span class="lineno">  408</span>&#160; </div>
<div class="line"><a name="l00409"></a><span class="lineno">  409</span>&#160;    EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR</div>
<div class="line"><a name="l00410"></a><span class="lineno">  410</span>&#160;    <span class="keyword">inline</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> rows() const EIGEN_NOEXCEPT { <span class="keywordflow">return</span> m_lu.rows(); }</div>
<div class="line"><a name="l00411"></a><span class="lineno">  411</span>&#160;    EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR</div>
<div class="line"><a name="l00412"></a><span class="lineno">  412</span>&#160;    <span class="keyword">inline</span> <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> cols() const EIGEN_NOEXCEPT { <span class="keywordflow">return</span> m_lu.cols(); }</div>
<div class="line"><a name="l00413"></a><span class="lineno">  413</span>&#160; </div>
<div class="line"><a name="l00414"></a><span class="lineno">  414</span>&#160;<span class="preprocessor">    #ifndef EIGEN_PARSED_BY_DOXYGEN</span></div>
<div class="line"><a name="l00415"></a><span class="lineno">  415</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> RhsType, <span class="keyword">typename</span> DstType&gt;</div>
<div class="line"><a name="l00416"></a><span class="lineno">  416</span>&#160;    <span class="keywordtype">void</span> _solve_impl(<span class="keyword">const</span> RhsType &amp;rhs, DstType &amp;dst) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00417"></a><span class="lineno">  417</span>&#160; </div>
<div class="line"><a name="l00418"></a><span class="lineno">  418</span>&#160;    <span class="keyword">template</span>&lt;<span class="keywordtype">bool</span> Conjugate, <span class="keyword">typename</span> RhsType, <span class="keyword">typename</span> DstType&gt;</div>
<div class="line"><a name="l00419"></a><span class="lineno">  419</span>&#160;    <span class="keywordtype">void</span> _solve_impl_transposed(<span class="keyword">const</span> RhsType &amp;rhs, DstType &amp;dst) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00420"></a><span class="lineno">  420</span>&#160;<span class="preprocessor">    #endif</span></div>
<div class="line"><a name="l00421"></a><span class="lineno">  421</span>&#160; </div>
<div class="line"><a name="l00422"></a><span class="lineno">  422</span>&#160;  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00423"></a><span class="lineno">  423</span>&#160; </div>
<div class="line"><a name="l00424"></a><span class="lineno">  424</span>&#160;    EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)</div>
<div class="line"><a name="l00425"></a><span class="lineno">  425</span>&#160; </div>
<div class="line"><a name="l00426"></a><span class="lineno">  426</span>&#160;    <span class="keywordtype">void</span> computeInPlace();</div>
<div class="line"><a name="l00427"></a><span class="lineno">  427</span>&#160; </div>
<div class="line"><a name="l00428"></a><span class="lineno">  428</span>&#160;    MatrixType m_lu;</div>
<div class="line"><a name="l00429"></a><span class="lineno">  429</span>&#160;    PermutationPType m_p;</div>
<div class="line"><a name="l00430"></a><span class="lineno">  430</span>&#160;    PermutationQType m_q;</div>
<div class="line"><a name="l00431"></a><span class="lineno">  431</span>&#160;    IntColVectorType m_rowsTranspositions;</div>
<div class="line"><a name="l00432"></a><span class="lineno">  432</span>&#160;    IntRowVectorType m_colsTranspositions;</div>
<div class="line"><a name="l00433"></a><span class="lineno">  433</span>&#160;    <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> m_nonzero_pivots;</div>
<div class="line"><a name="l00434"></a><span class="lineno">  434</span>&#160;    RealScalar m_l1_norm;</div>
<div class="line"><a name="l00435"></a><span class="lineno">  435</span>&#160;    RealScalar m_maxpivot, m_prescribedThreshold;</div>
<div class="line"><a name="l00436"></a><span class="lineno">  436</span>&#160;    <span class="keywordtype">signed</span> <span class="keywordtype">char</span> m_det_pq;</div>
<div class="line"><a name="l00437"></a><span class="lineno">  437</span>&#160;    <span class="keywordtype">bool</span> m_isInitialized, m_usePrescribedThreshold;</div>
<div class="line"><a name="l00438"></a><span class="lineno">  438</span>&#160;};</div>
<div class="line"><a name="l00439"></a><span class="lineno">  439</span>&#160; </div>
<div class="line"><a name="l00440"></a><span class="lineno">  440</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00441"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#af225528d1c6e623a2b1dce091907d13e">  441</a></span>&#160;<a class="code" href="classEigen_1_1FullPivLU.html#af225528d1c6e623a2b1dce091907d13e">FullPivLU&lt;MatrixType&gt;::FullPivLU</a>()</div>
<div class="line"><a name="l00442"></a><span class="lineno">  442</span>&#160;  : m_isInitialized(false), m_usePrescribedThreshold(false)</div>
<div class="line"><a name="l00443"></a><span class="lineno">  443</span>&#160;{</div>
<div class="line"><a name="l00444"></a><span class="lineno">  444</span>&#160;}</div>
<div class="line"><a name="l00445"></a><span class="lineno">  445</span>&#160; </div>
<div class="line"><a name="l00446"></a><span class="lineno">  446</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00447"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#ae83ebd2a24088f04e3ac835b0dc001e1">  447</a></span>&#160;<a class="code" href="classEigen_1_1FullPivLU.html#af225528d1c6e623a2b1dce091907d13e">FullPivLU&lt;MatrixType&gt;::FullPivLU</a>(<a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> rows, <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> cols)</div>
<div class="line"><a name="l00448"></a><span class="lineno">  448</span>&#160;  : m_lu(rows, cols),</div>
<div class="line"><a name="l00449"></a><span class="lineno">  449</span>&#160;    m_p(rows),</div>
<div class="line"><a name="l00450"></a><span class="lineno">  450</span>&#160;    m_q(cols),</div>
<div class="line"><a name="l00451"></a><span class="lineno">  451</span>&#160;    m_rowsTranspositions(rows),</div>
<div class="line"><a name="l00452"></a><span class="lineno">  452</span>&#160;    m_colsTranspositions(cols),</div>
<div class="line"><a name="l00453"></a><span class="lineno">  453</span>&#160;    m_isInitialized(false),</div>
<div class="line"><a name="l00454"></a><span class="lineno">  454</span>&#160;    m_usePrescribedThreshold(false)</div>
<div class="line"><a name="l00455"></a><span class="lineno">  455</span>&#160;{</div>
<div class="line"><a name="l00456"></a><span class="lineno">  456</span>&#160;}</div>
<div class="line"><a name="l00457"></a><span class="lineno">  457</span>&#160; </div>
<div class="line"><a name="l00458"></a><span class="lineno">  458</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00459"></a><span class="lineno">  459</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> InputType&gt;</div>
<div class="line"><a name="l00460"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a31a6a984478a9f721f367667fe4c5ab1">  460</a></span>&#160;<a class="code" href="classEigen_1_1FullPivLU.html#af225528d1c6e623a2b1dce091907d13e">FullPivLU&lt;MatrixType&gt;::FullPivLU</a>(<span class="keyword">const</span> <a class="code" href="structEigen_1_1EigenBase.html">EigenBase&lt;InputType&gt;</a>&amp; matrix)</div>
<div class="line"><a name="l00461"></a><span class="lineno">  461</span>&#160;  : m_lu(matrix.rows(), matrix.cols()),</div>
<div class="line"><a name="l00462"></a><span class="lineno">  462</span>&#160;    m_p(matrix.rows()),</div>
<div class="line"><a name="l00463"></a><span class="lineno">  463</span>&#160;    m_q(matrix.cols()),</div>
<div class="line"><a name="l00464"></a><span class="lineno">  464</span>&#160;    m_rowsTranspositions(matrix.rows()),</div>
<div class="line"><a name="l00465"></a><span class="lineno">  465</span>&#160;    m_colsTranspositions(matrix.cols()),</div>
<div class="line"><a name="l00466"></a><span class="lineno">  466</span>&#160;    m_isInitialized(false),</div>
<div class="line"><a name="l00467"></a><span class="lineno">  467</span>&#160;    m_usePrescribedThreshold(false)</div>
<div class="line"><a name="l00468"></a><span class="lineno">  468</span>&#160;{</div>
<div class="line"><a name="l00469"></a><span class="lineno">  469</span>&#160;  <a class="code" href="classEigen_1_1FullPivLU.html#a396f63d737e0613f41004e30be8fe3cf">compute</a>(matrix.<a class="code" href="structEigen_1_1EigenBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">derived</a>());</div>
<div class="line"><a name="l00470"></a><span class="lineno">  470</span>&#160;}</div>
<div class="line"><a name="l00471"></a><span class="lineno">  471</span>&#160; </div>
<div class="line"><a name="l00472"></a><span class="lineno">  472</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00473"></a><span class="lineno">  473</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> InputType&gt;</div>
<div class="line"><a name="l00474"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a3e903b9f401e3fc5d1ca7c6951c76185">  474</a></span>&#160;<a class="code" href="classEigen_1_1FullPivLU.html#af225528d1c6e623a2b1dce091907d13e">FullPivLU&lt;MatrixType&gt;::FullPivLU</a>(<a class="code" href="structEigen_1_1EigenBase.html">EigenBase&lt;InputType&gt;</a>&amp; matrix)</div>
<div class="line"><a name="l00475"></a><span class="lineno">  475</span>&#160;  : m_lu(matrix.derived()),</div>
<div class="line"><a name="l00476"></a><span class="lineno">  476</span>&#160;    m_p(matrix.rows()),</div>
<div class="line"><a name="l00477"></a><span class="lineno">  477</span>&#160;    m_q(matrix.cols()),</div>
<div class="line"><a name="l00478"></a><span class="lineno">  478</span>&#160;    m_rowsTranspositions(matrix.rows()),</div>
<div class="line"><a name="l00479"></a><span class="lineno">  479</span>&#160;    m_colsTranspositions(matrix.cols()),</div>
<div class="line"><a name="l00480"></a><span class="lineno">  480</span>&#160;    m_isInitialized(false),</div>
<div class="line"><a name="l00481"></a><span class="lineno">  481</span>&#160;    m_usePrescribedThreshold(false)</div>
<div class="line"><a name="l00482"></a><span class="lineno">  482</span>&#160;{</div>
<div class="line"><a name="l00483"></a><span class="lineno">  483</span>&#160;  computeInPlace();</div>
<div class="line"><a name="l00484"></a><span class="lineno">  484</span>&#160;}</div>
<div class="line"><a name="l00485"></a><span class="lineno">  485</span>&#160; </div>
<div class="line"><a name="l00486"></a><span class="lineno">  486</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00487"></a><span class="lineno">  487</span>&#160;<span class="keywordtype">void</span> <a class="code" href="classEigen_1_1FullPivLU.html">FullPivLU&lt;MatrixType&gt;::computeInPlace</a>()</div>
<div class="line"><a name="l00488"></a><span class="lineno">  488</span>&#160;{</div>
<div class="line"><a name="l00489"></a><span class="lineno">  489</span>&#160;  <span class="comment">// the permutations are stored as int indices, so just to be sure:</span></div>
<div class="line"><a name="l00490"></a><span class="lineno">  490</span>&#160;  eigen_assert(m_lu.rows()&lt;=<a class="code" href="structEigen_1_1NumTraits.html">NumTraits&lt;int&gt;::highest</a>() &amp;&amp; m_lu.cols()&lt;=<a class="code" href="structEigen_1_1NumTraits.html">NumTraits&lt;int&gt;::highest</a>());</div>
<div class="line"><a name="l00491"></a><span class="lineno">  491</span>&#160; </div>
<div class="line"><a name="l00492"></a><span class="lineno">  492</span>&#160;  m_l1_norm = m_lu.cwiseAbs().colwise().sum().maxCoeff();</div>
<div class="line"><a name="l00493"></a><span class="lineno">  493</span>&#160; </div>
<div class="line"><a name="l00494"></a><span class="lineno">  494</span>&#160;  <span class="keyword">const</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> size = m_lu.diagonalSize();</div>
<div class="line"><a name="l00495"></a><span class="lineno">  495</span>&#160;  <span class="keyword">const</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> rows = m_lu.rows();</div>
<div class="line"><a name="l00496"></a><span class="lineno">  496</span>&#160;  <span class="keyword">const</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> cols = m_lu.cols();</div>
<div class="line"><a name="l00497"></a><span class="lineno">  497</span>&#160; </div>
<div class="line"><a name="l00498"></a><span class="lineno">  498</span>&#160;  <span class="comment">// will store the transpositions, before we accumulate them at the end.</span></div>
<div class="line"><a name="l00499"></a><span class="lineno">  499</span>&#160;  <span class="comment">// can&#39;t accumulate on-the-fly because that will be done in reverse order for the rows.</span></div>
<div class="line"><a name="l00500"></a><span class="lineno">  500</span>&#160;  m_rowsTranspositions.resize(m_lu.rows());</div>
<div class="line"><a name="l00501"></a><span class="lineno">  501</span>&#160;  m_colsTranspositions.resize(m_lu.cols());</div>
<div class="line"><a name="l00502"></a><span class="lineno">  502</span>&#160;  <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> number_of_transpositions = 0; <span class="comment">// number of NONTRIVIAL transpositions, i.e. m_rowsTranspositions[i]!=i</span></div>
<div class="line"><a name="l00503"></a><span class="lineno">  503</span>&#160; </div>
<div class="line"><a name="l00504"></a><span class="lineno">  504</span>&#160;  m_nonzero_pivots = size; <span class="comment">// the generic case is that in which all pivots are nonzero (invertible case)</span></div>
<div class="line"><a name="l00505"></a><span class="lineno">  505</span>&#160;  m_maxpivot = RealScalar(0);</div>
<div class="line"><a name="l00506"></a><span class="lineno">  506</span>&#160; </div>
<div class="line"><a name="l00507"></a><span class="lineno">  507</span>&#160;  <span class="keywordflow">for</span>(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> k = 0; k &lt; size; ++k)</div>
<div class="line"><a name="l00508"></a><span class="lineno">  508</span>&#160;  {</div>
<div class="line"><a name="l00509"></a><span class="lineno">  509</span>&#160;    <span class="comment">// First, we need to find the pivot.</span></div>
<div class="line"><a name="l00510"></a><span class="lineno">  510</span>&#160; </div>
<div class="line"><a name="l00511"></a><span class="lineno">  511</span>&#160;    <span class="comment">// biggest coefficient in the remaining bottom-right corner (starting at row k, col k)</span></div>
<div class="line"><a name="l00512"></a><span class="lineno">  512</span>&#160;    <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> row_of_biggest_in_corner, col_of_biggest_in_corner;</div>
<div class="line"><a name="l00513"></a><span class="lineno">  513</span>&#160;    <span class="keyword">typedef</span> internal::scalar_score_coeff_op&lt;Scalar&gt; Scoring;</div>
<div class="line"><a name="l00514"></a><span class="lineno">  514</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> Scoring::result_type Score;</div>
<div class="line"><a name="l00515"></a><span class="lineno">  515</span>&#160;    Score biggest_in_corner;</div>
<div class="line"><a name="l00516"></a><span class="lineno">  516</span>&#160;    biggest_in_corner = m_lu.bottomRightCorner(rows-k, cols-k)</div>
<div class="line"><a name="l00517"></a><span class="lineno">  517</span>&#160;                        .unaryExpr(Scoring())</div>
<div class="line"><a name="l00518"></a><span class="lineno">  518</span>&#160;                        .maxCoeff(&amp;row_of_biggest_in_corner, &amp;col_of_biggest_in_corner);</div>
<div class="line"><a name="l00519"></a><span class="lineno">  519</span>&#160;    row_of_biggest_in_corner += k; <span class="comment">// correct the values! since they were computed in the corner,</span></div>
<div class="line"><a name="l00520"></a><span class="lineno">  520</span>&#160;    col_of_biggest_in_corner += k; <span class="comment">// need to add k to them.</span></div>
<div class="line"><a name="l00521"></a><span class="lineno">  521</span>&#160; </div>
<div class="line"><a name="l00522"></a><span class="lineno">  522</span>&#160;    <span class="keywordflow">if</span>(numext::is_exactly_zero(biggest_in_corner))</div>
<div class="line"><a name="l00523"></a><span class="lineno">  523</span>&#160;    {</div>
<div class="line"><a name="l00524"></a><span class="lineno">  524</span>&#160;      <span class="comment">// before exiting, make sure to initialize the still uninitialized transpositions</span></div>
<div class="line"><a name="l00525"></a><span class="lineno">  525</span>&#160;      <span class="comment">// in a sane state without destroying what we already have.</span></div>
<div class="line"><a name="l00526"></a><span class="lineno">  526</span>&#160;      m_nonzero_pivots = k;</div>
<div class="line"><a name="l00527"></a><span class="lineno">  527</span>&#160;      <span class="keywordflow">for</span>(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = k; i &lt; size; ++i)</div>
<div class="line"><a name="l00528"></a><span class="lineno">  528</span>&#160;      {</div>
<div class="line"><a name="l00529"></a><span class="lineno">  529</span>&#160;        m_rowsTranspositions.coeffRef(i) = internal::convert_index&lt;StorageIndex&gt;(i);</div>
<div class="line"><a name="l00530"></a><span class="lineno">  530</span>&#160;        m_colsTranspositions.coeffRef(i) = internal::convert_index&lt;StorageIndex&gt;(i);</div>
<div class="line"><a name="l00531"></a><span class="lineno">  531</span>&#160;      }</div>
<div class="line"><a name="l00532"></a><span class="lineno">  532</span>&#160;      <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00533"></a><span class="lineno">  533</span>&#160;    }</div>
<div class="line"><a name="l00534"></a><span class="lineno">  534</span>&#160; </div>
<div class="line"><a name="l00535"></a><span class="lineno">  535</span>&#160;    RealScalar abs_pivot = internal::abs_knowing_score&lt;Scalar&gt;()(m_lu(row_of_biggest_in_corner, col_of_biggest_in_corner), biggest_in_corner);</div>
<div class="line"><a name="l00536"></a><span class="lineno">  536</span>&#160;    <span class="keywordflow">if</span>(abs_pivot &gt; m_maxpivot) m_maxpivot = abs_pivot;</div>
<div class="line"><a name="l00537"></a><span class="lineno">  537</span>&#160; </div>
<div class="line"><a name="l00538"></a><span class="lineno">  538</span>&#160;    <span class="comment">// Now that we&#39;ve found the pivot, we need to apply the row/col swaps to</span></div>
<div class="line"><a name="l00539"></a><span class="lineno">  539</span>&#160;    <span class="comment">// bring it to the location (k,k).</span></div>
<div class="line"><a name="l00540"></a><span class="lineno">  540</span>&#160; </div>
<div class="line"><a name="l00541"></a><span class="lineno">  541</span>&#160;    m_rowsTranspositions.coeffRef(k) = internal::convert_index&lt;StorageIndex&gt;(row_of_biggest_in_corner);</div>
<div class="line"><a name="l00542"></a><span class="lineno">  542</span>&#160;    m_colsTranspositions.coeffRef(k) = internal::convert_index&lt;StorageIndex&gt;(col_of_biggest_in_corner);</div>
<div class="line"><a name="l00543"></a><span class="lineno">  543</span>&#160;    <span class="keywordflow">if</span>(k != row_of_biggest_in_corner) {</div>
<div class="line"><a name="l00544"></a><span class="lineno">  544</span>&#160;      m_lu.row(k).swap(m_lu.row(row_of_biggest_in_corner));</div>
<div class="line"><a name="l00545"></a><span class="lineno">  545</span>&#160;      ++number_of_transpositions;</div>
<div class="line"><a name="l00546"></a><span class="lineno">  546</span>&#160;    }</div>
<div class="line"><a name="l00547"></a><span class="lineno">  547</span>&#160;    <span class="keywordflow">if</span>(k != col_of_biggest_in_corner) {</div>
<div class="line"><a name="l00548"></a><span class="lineno">  548</span>&#160;      m_lu.col(k).swap(m_lu.col(col_of_biggest_in_corner));</div>
<div class="line"><a name="l00549"></a><span class="lineno">  549</span>&#160;      ++number_of_transpositions;</div>
<div class="line"><a name="l00550"></a><span class="lineno">  550</span>&#160;    }</div>
<div class="line"><a name="l00551"></a><span class="lineno">  551</span>&#160; </div>
<div class="line"><a name="l00552"></a><span class="lineno">  552</span>&#160;    <span class="comment">// Now that the pivot is at the right location, we update the remaining</span></div>
<div class="line"><a name="l00553"></a><span class="lineno">  553</span>&#160;    <span class="comment">// bottom-right corner by Gaussian elimination.</span></div>
<div class="line"><a name="l00554"></a><span class="lineno">  554</span>&#160; </div>
<div class="line"><a name="l00555"></a><span class="lineno">  555</span>&#160;    <span class="keywordflow">if</span>(k&lt;rows-1)</div>
<div class="line"><a name="l00556"></a><span class="lineno">  556</span>&#160;      m_lu.col(k).tail(rows-k-1) /= m_lu.coeff(k,k);</div>
<div class="line"><a name="l00557"></a><span class="lineno">  557</span>&#160;    <span class="keywordflow">if</span>(k&lt;size-1)</div>
<div class="line"><a name="l00558"></a><span class="lineno">  558</span>&#160;      m_lu.block(k+1,k+1,rows-k-1,cols-k-1).noalias() -= m_lu.col(k).tail(rows-k-1) * m_lu.row(k).tail(cols-k-1);</div>
<div class="line"><a name="l00559"></a><span class="lineno">  559</span>&#160;  }</div>
<div class="line"><a name="l00560"></a><span class="lineno">  560</span>&#160; </div>
<div class="line"><a name="l00561"></a><span class="lineno">  561</span>&#160;  <span class="comment">// the main loop is over, we still have to accumulate the transpositions to find the</span></div>
<div class="line"><a name="l00562"></a><span class="lineno">  562</span>&#160;  <span class="comment">// permutations P and Q</span></div>
<div class="line"><a name="l00563"></a><span class="lineno">  563</span>&#160; </div>
<div class="line"><a name="l00564"></a><span class="lineno">  564</span>&#160;  m_p.setIdentity(rows);</div>
<div class="line"><a name="l00565"></a><span class="lineno">  565</span>&#160;  <span class="keywordflow">for</span>(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> k = size-1; k &gt;= 0; --k)</div>
<div class="line"><a name="l00566"></a><span class="lineno">  566</span>&#160;    m_p.applyTranspositionOnTheRight(k, m_rowsTranspositions.coeff(k));</div>
<div class="line"><a name="l00567"></a><span class="lineno">  567</span>&#160; </div>
<div class="line"><a name="l00568"></a><span class="lineno">  568</span>&#160;  m_q.setIdentity(cols);</div>
<div class="line"><a name="l00569"></a><span class="lineno">  569</span>&#160;  <span class="keywordflow">for</span>(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> k = 0; k &lt; size; ++k)</div>
<div class="line"><a name="l00570"></a><span class="lineno">  570</span>&#160;    m_q.applyTranspositionOnTheRight(k, m_colsTranspositions.coeff(k));</div>
<div class="line"><a name="l00571"></a><span class="lineno">  571</span>&#160; </div>
<div class="line"><a name="l00572"></a><span class="lineno">  572</span>&#160;  m_det_pq = (number_of_transpositions%2) ? -1 : 1;</div>
<div class="line"><a name="l00573"></a><span class="lineno">  573</span>&#160; </div>
<div class="line"><a name="l00574"></a><span class="lineno">  574</span>&#160;  m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00575"></a><span class="lineno">  575</span>&#160;}</div>
<div class="line"><a name="l00576"></a><span class="lineno">  576</span>&#160; </div>
<div class="line"><a name="l00577"></a><span class="lineno">  577</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00578"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a71654e5c60a26407ecccfaa5b34bb0aa">  578</a></span>&#160;<span class="keyword">typename</span> internal::traits&lt;MatrixType&gt;::Scalar <a class="code" href="classEigen_1_1FullPivLU.html#a71654e5c60a26407ecccfaa5b34bb0aa">FullPivLU&lt;MatrixType&gt;::determinant</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00579"></a><span class="lineno">  579</span>&#160;<span class="keyword"></span>{</div>
<div class="line"><a name="l00580"></a><span class="lineno">  580</span>&#160;  eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;LU is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00581"></a><span class="lineno">  581</span>&#160;  eigen_assert(m_lu.rows() == m_lu.cols() &amp;&amp; <span class="stringliteral">&quot;You can&#39;t take the determinant of a non-square matrix!&quot;</span>);</div>
<div class="line"><a name="l00582"></a><span class="lineno">  582</span>&#160;  <span class="keywordflow">return</span> Scalar(m_det_pq) * Scalar(m_lu.diagonal().prod());</div>
<div class="line"><a name="l00583"></a><span class="lineno">  583</span>&#160;}</div>
<div class="line"><a name="l00584"></a><span class="lineno">  584</span>&#160; </div>
<div class="line"><a name="l00588"></a><span class="lineno">  588</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00589"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a191a4f598b0c192a83ab48984e87ee51">  589</a></span>&#160;MatrixType <a class="code" href="classEigen_1_1FullPivLU.html#a191a4f598b0c192a83ab48984e87ee51">FullPivLU&lt;MatrixType&gt;::reconstructedMatrix</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00590"></a><span class="lineno">  590</span>&#160;<span class="keyword"></span>{</div>
<div class="line"><a name="l00591"></a><span class="lineno">  591</span>&#160;  eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;LU is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00592"></a><span class="lineno">  592</span>&#160;  <span class="keyword">const</span> <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> smalldim = (std::min)(m_lu.rows(), m_lu.cols());</div>
<div class="line"><a name="l00593"></a><span class="lineno">  593</span>&#160;  <span class="comment">// LU</span></div>
<div class="line"><a name="l00594"></a><span class="lineno">  594</span>&#160;  MatrixType res(m_lu.rows(),m_lu.cols());</div>
<div class="line"><a name="l00595"></a><span class="lineno">  595</span>&#160;  <span class="comment">// FIXME the .toDenseMatrix() should not be needed...</span></div>
<div class="line"><a name="l00596"></a><span class="lineno">  596</span>&#160;  res = m_lu.leftCols(smalldim)</div>
<div class="line"><a name="l00597"></a><span class="lineno">  597</span>&#160;            .template triangularView&lt;UnitLower&gt;().toDenseMatrix()</div>
<div class="line"><a name="l00598"></a><span class="lineno">  598</span>&#160;      * m_lu.topRows(smalldim)</div>
<div class="line"><a name="l00599"></a><span class="lineno">  599</span>&#160;            .template triangularView&lt;Upper&gt;().toDenseMatrix();</div>
<div class="line"><a name="l00600"></a><span class="lineno">  600</span>&#160; </div>
<div class="line"><a name="l00601"></a><span class="lineno">  601</span>&#160;  <span class="comment">// P^{-1}(LU)</span></div>
<div class="line"><a name="l00602"></a><span class="lineno">  602</span>&#160;  res = m_p.inverse() * res;</div>
<div class="line"><a name="l00603"></a><span class="lineno">  603</span>&#160; </div>
<div class="line"><a name="l00604"></a><span class="lineno">  604</span>&#160;  <span class="comment">// (P^{-1}LU)Q^{-1}</span></div>
<div class="line"><a name="l00605"></a><span class="lineno">  605</span>&#160;  res = res * m_q.inverse();</div>
<div class="line"><a name="l00606"></a><span class="lineno">  606</span>&#160; </div>
<div class="line"><a name="l00607"></a><span class="lineno">  607</span>&#160;  <span class="keywordflow">return</span> res;</div>
<div class="line"><a name="l00608"></a><span class="lineno">  608</span>&#160;}</div>
<div class="line"><a name="l00609"></a><span class="lineno">  609</span>&#160; </div>
<div class="line"><a name="l00610"></a><span class="lineno">  610</span>&#160;<span class="comment">/********* Implementation of kernel() **************************************************/</span></div>
<div class="line"><a name="l00611"></a><span class="lineno">  611</span>&#160; </div>
<div class="line"><a name="l00612"></a><span class="lineno">  612</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00613"></a><span class="lineno">  613</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType_&gt;</div>
<div class="line"><a name="l00614"></a><span class="lineno">  614</span>&#160;<span class="keyword">struct </span>kernel_retval&lt;<a class="code" href="classEigen_1_1FullPivLU.html">FullPivLU</a>&lt;MatrixType_&gt; &gt;</div>
<div class="line"><a name="l00615"></a><span class="lineno">  615</span>&#160;  : kernel_retval_base&lt;FullPivLU&lt;MatrixType_&gt; &gt;</div>
<div class="line"><a name="l00616"></a><span class="lineno">  616</span>&#160;{</div>
<div class="line"><a name="l00617"></a><span class="lineno">  617</span>&#160;  EIGEN_MAKE_KERNEL_HELPERS(<a class="code" href="classEigen_1_1FullPivLU.html">FullPivLU&lt;MatrixType_&gt;</a>)</div>
<div class="line"><a name="l00618"></a><span class="lineno">  618</span>&#160; </div>
<div class="line"><a name="l00619"></a><span class="lineno">  619</span>&#160;  <span class="keyword">enum</span> { MaxSmallDimAtCompileTime = min_size_prefer_fixed(</div>
<div class="line"><a name="l00620"></a><span class="lineno">  620</span>&#160;              MatrixType::MaxColsAtCompileTime,</div>
<div class="line"><a name="l00621"></a><span class="lineno">  621</span>&#160;              MatrixType::MaxRowsAtCompileTime)</div>
<div class="line"><a name="l00622"></a><span class="lineno">  622</span>&#160;  };</div>
<div class="line"><a name="l00623"></a><span class="lineno">  623</span>&#160; </div>
<div class="line"><a name="l00624"></a><span class="lineno">  624</span>&#160;  <span class="keyword">template</span>&lt;<span class="keyword">typename</span> Dest&gt; <span class="keywordtype">void</span> evalTo(Dest&amp; dst)<span class="keyword"> const</span></div>
<div class="line"><a name="l00625"></a><span class="lineno">  625</span>&#160;<span class="keyword">  </span>{</div>
<div class="line"><a name="l00626"></a><span class="lineno">  626</span>&#160;    <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00627"></a><span class="lineno">  627</span>&#160;    <span class="keyword">const</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> cols = dec().matrixLU().cols(), dimker = cols - rank();</div>
<div class="line"><a name="l00628"></a><span class="lineno">  628</span>&#160;    <span class="keywordflow">if</span>(dimker == 0)</div>
<div class="line"><a name="l00629"></a><span class="lineno">  629</span>&#160;    {</div>
<div class="line"><a name="l00630"></a><span class="lineno">  630</span>&#160;      <span class="comment">// The Kernel is just {0}, so it doesn&#39;t have a basis properly speaking, but let&#39;s</span></div>
<div class="line"><a name="l00631"></a><span class="lineno">  631</span>&#160;      <span class="comment">// avoid crashing/asserting as that depends on floating point calculations. Let&#39;s</span></div>
<div class="line"><a name="l00632"></a><span class="lineno">  632</span>&#160;      <span class="comment">// just return a single column vector filled with zeros.</span></div>
<div class="line"><a name="l00633"></a><span class="lineno">  633</span>&#160;      dst.setZero();</div>
<div class="line"><a name="l00634"></a><span class="lineno">  634</span>&#160;      <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00635"></a><span class="lineno">  635</span>&#160;    }</div>
<div class="line"><a name="l00636"></a><span class="lineno">  636</span>&#160; </div>
<div class="line"><a name="l00637"></a><span class="lineno">  637</span>&#160;    <span class="comment">/* Let us use the following lemma:</span></div>
<div class="line"><a name="l00638"></a><span class="lineno">  638</span>&#160;<span class="comment">      *</span></div>
<div class="line"><a name="l00639"></a><span class="lineno">  639</span>&#160;<span class="comment">      * Lemma: If the matrix A has the LU decomposition PAQ = LU,</span></div>
<div class="line"><a name="l00640"></a><span class="lineno">  640</span>&#160;<span class="comment">      * then Ker A = Q(Ker U).</span></div>
<div class="line"><a name="l00641"></a><span class="lineno">  641</span>&#160;<span class="comment">      *</span></div>
<div class="line"><a name="l00642"></a><span class="lineno">  642</span>&#160;<span class="comment">      * Proof: trivial: just keep in mind that P, Q, L are invertible.</span></div>
<div class="line"><a name="l00643"></a><span class="lineno">  643</span>&#160;<span class="comment">      */</span></div>
<div class="line"><a name="l00644"></a><span class="lineno">  644</span>&#160; </div>
<div class="line"><a name="l00645"></a><span class="lineno">  645</span>&#160;    <span class="comment">/* Thus, all we need to do is to compute Ker U, and then apply Q.</span></div>
<div class="line"><a name="l00646"></a><span class="lineno">  646</span>&#160;<span class="comment">      *</span></div>
<div class="line"><a name="l00647"></a><span class="lineno">  647</span>&#160;<span class="comment">      * U is upper triangular, with eigenvalues sorted so that any zeros appear at the end.</span></div>
<div class="line"><a name="l00648"></a><span class="lineno">  648</span>&#160;<span class="comment">      * Thus, the diagonal of U ends with exactly</span></div>
<div class="line"><a name="l00649"></a><span class="lineno">  649</span>&#160;<span class="comment">      * dimKer zero&#39;s. Let us use that to construct dimKer linearly</span></div>
<div class="line"><a name="l00650"></a><span class="lineno">  650</span>&#160;<span class="comment">      * independent vectors in Ker U.</span></div>
<div class="line"><a name="l00651"></a><span class="lineno">  651</span>&#160;<span class="comment">      */</span></div>
<div class="line"><a name="l00652"></a><span class="lineno">  652</span>&#160; </div>
<div class="line"><a name="l00653"></a><span class="lineno">  653</span>&#160;    Matrix&lt;Index, Dynamic, 1, 0, MaxSmallDimAtCompileTime, 1&gt; pivots(rank());</div>
<div class="line"><a name="l00654"></a><span class="lineno">  654</span>&#160;    RealScalar premultiplied_threshold = dec().maxPivot() * dec().threshold();</div>
<div class="line"><a name="l00655"></a><span class="lineno">  655</span>&#160;    <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> p = 0;</div>
<div class="line"><a name="l00656"></a><span class="lineno">  656</span>&#160;    <span class="keywordflow">for</span>(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = 0; i &lt; dec().nonzeroPivots(); ++i)</div>
<div class="line"><a name="l00657"></a><span class="lineno">  657</span>&#160;      <span class="keywordflow">if</span>(<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(dec().matrixLU().coeff(i,i)) &gt; premultiplied_threshold)</div>
<div class="line"><a name="l00658"></a><span class="lineno">  658</span>&#160;        pivots.coeffRef(p++) = i;</div>
<div class="line"><a name="l00659"></a><span class="lineno">  659</span>&#160;    eigen_internal_assert(p == rank());</div>
<div class="line"><a name="l00660"></a><span class="lineno">  660</span>&#160; </div>
<div class="line"><a name="l00661"></a><span class="lineno">  661</span>&#160;    <span class="comment">// we construct a temporaty trapezoid matrix m, by taking the U matrix and</span></div>
<div class="line"><a name="l00662"></a><span class="lineno">  662</span>&#160;    <span class="comment">// permuting the rows and cols to bring the nonnegligible pivots to the top of</span></div>
<div class="line"><a name="l00663"></a><span class="lineno">  663</span>&#160;    <span class="comment">// the main diagonal. We need that to be able to apply our triangular solvers.</span></div>
<div class="line"><a name="l00664"></a><span class="lineno">  664</span>&#160;    <span class="comment">// FIXME when we get triangularView-for-rectangular-matrices, this can be simplified</span></div>
<div class="line"><a name="l00665"></a><span class="lineno">  665</span>&#160;    Matrix&lt;<span class="keyword">typename</span> MatrixType::Scalar, <a class="code" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a>, <a class="code" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a>, MatrixType::Options,</div>
<div class="line"><a name="l00666"></a><span class="lineno">  666</span>&#160;           MaxSmallDimAtCompileTime, MatrixType::MaxColsAtCompileTime&gt;</div>
<div class="line"><a name="l00667"></a><span class="lineno">  667</span>&#160;      m(dec().matrixLU().block(0, 0, rank(), cols));</div>
<div class="line"><a name="l00668"></a><span class="lineno">  668</span>&#160;    <span class="keywordflow">for</span>(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = 0; i &lt; rank(); ++i)</div>
<div class="line"><a name="l00669"></a><span class="lineno">  669</span>&#160;    {</div>
<div class="line"><a name="l00670"></a><span class="lineno">  670</span>&#160;      <span class="keywordflow">if</span>(i) m.row(i).head(i).setZero();</div>
<div class="line"><a name="l00671"></a><span class="lineno">  671</span>&#160;      m.row(i).tail(cols-i) = dec().matrixLU().row(pivots.coeff(i)).tail(cols-i);</div>
<div class="line"><a name="l00672"></a><span class="lineno">  672</span>&#160;    }</div>
<div class="line"><a name="l00673"></a><span class="lineno">  673</span>&#160;    m.block(0, 0, rank(), rank());</div>
<div class="line"><a name="l00674"></a><span class="lineno">  674</span>&#160;    m.block(0, 0, rank(), rank()).template triangularView&lt;StrictlyLower&gt;().setZero();</div>
<div class="line"><a name="l00675"></a><span class="lineno">  675</span>&#160;    <span class="keywordflow">for</span>(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = 0; i &lt; rank(); ++i)</div>
<div class="line"><a name="l00676"></a><span class="lineno">  676</span>&#160;      m.col(i).swap(m.col(pivots.coeff(i)));</div>
<div class="line"><a name="l00677"></a><span class="lineno">  677</span>&#160; </div>
<div class="line"><a name="l00678"></a><span class="lineno">  678</span>&#160;    <span class="comment">// ok, we have our trapezoid matrix, we can apply the triangular solver.</span></div>
<div class="line"><a name="l00679"></a><span class="lineno">  679</span>&#160;    <span class="comment">// notice that the math behind this suggests that we should apply this to the</span></div>
<div class="line"><a name="l00680"></a><span class="lineno">  680</span>&#160;    <span class="comment">// negative of the RHS, but for performance we just put the negative sign elsewhere, see below.</span></div>
<div class="line"><a name="l00681"></a><span class="lineno">  681</span>&#160;    m.topLeftCorner(rank(), rank())</div>
<div class="line"><a name="l00682"></a><span class="lineno">  682</span>&#160;     .<span class="keyword">template</span> triangularView&lt;Upper&gt;().solveInPlace(</div>
<div class="line"><a name="l00683"></a><span class="lineno">  683</span>&#160;        m.topRightCorner(rank(), dimker)</div>
<div class="line"><a name="l00684"></a><span class="lineno">  684</span>&#160;      );</div>
<div class="line"><a name="l00685"></a><span class="lineno">  685</span>&#160; </div>
<div class="line"><a name="l00686"></a><span class="lineno">  686</span>&#160;    <span class="comment">// now we must undo the column permutation that we had applied!</span></div>
<div class="line"><a name="l00687"></a><span class="lineno">  687</span>&#160;    <span class="keywordflow">for</span>(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = rank()-1; i &gt;= 0; --i)</div>
<div class="line"><a name="l00688"></a><span class="lineno">  688</span>&#160;      m.col(i).swap(m.col(pivots.coeff(i)));</div>
<div class="line"><a name="l00689"></a><span class="lineno">  689</span>&#160; </div>
<div class="line"><a name="l00690"></a><span class="lineno">  690</span>&#160;    <span class="comment">// see the negative sign in the next line, that&#39;s what we were talking about above.</span></div>
<div class="line"><a name="l00691"></a><span class="lineno">  691</span>&#160;    <span class="keywordflow">for</span>(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = 0; i &lt; rank(); ++i) dst.row(dec().permutationQ().indices().coeff(i)) = -m.row(i).tail(dimker);</div>
<div class="line"><a name="l00692"></a><span class="lineno">  692</span>&#160;    <span class="keywordflow">for</span>(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = rank(); i &lt; cols; ++i) dst.row(dec().permutationQ().indices().coeff(i)).setZero();</div>
<div class="line"><a name="l00693"></a><span class="lineno">  693</span>&#160;    <span class="keywordflow">for</span>(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> k = 0; k &lt; dimker; ++k) dst.coeffRef(dec().permutationQ().indices().coeff(rank()+k), k) = Scalar(1);</div>
<div class="line"><a name="l00694"></a><span class="lineno">  694</span>&#160;  }</div>
<div class="line"><a name="l00695"></a><span class="lineno">  695</span>&#160;};</div>
<div class="line"><a name="l00696"></a><span class="lineno">  696</span>&#160; </div>
<div class="line"><a name="l00697"></a><span class="lineno">  697</span>&#160;<span class="comment">/***** Implementation of image() *****************************************************/</span></div>
<div class="line"><a name="l00698"></a><span class="lineno">  698</span>&#160; </div>
<div class="line"><a name="l00699"></a><span class="lineno">  699</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType_&gt;</div>
<div class="line"><a name="l00700"></a><span class="lineno">  700</span>&#160;<span class="keyword">struct </span>image_retval&lt;FullPivLU&lt;MatrixType_&gt; &gt;</div>
<div class="line"><a name="l00701"></a><span class="lineno">  701</span>&#160;  : image_retval_base&lt;FullPivLU&lt;MatrixType_&gt; &gt;</div>
<div class="line"><a name="l00702"></a><span class="lineno">  702</span>&#160;{</div>
<div class="line"><a name="l00703"></a><span class="lineno">  703</span>&#160;  EIGEN_MAKE_IMAGE_HELPERS(FullPivLU&lt;MatrixType_&gt;)</div>
<div class="line"><a name="l00704"></a><span class="lineno">  704</span>&#160; </div>
<div class="line"><a name="l00705"></a><span class="lineno">  705</span>&#160;  <span class="keyword">enum</span> { MaxSmallDimAtCompileTime = min_size_prefer_fixed(</div>
<div class="line"><a name="l00706"></a><span class="lineno">  706</span>&#160;              MatrixType::MaxColsAtCompileTime,</div>
<div class="line"><a name="l00707"></a><span class="lineno">  707</span>&#160;              MatrixType::MaxRowsAtCompileTime)</div>
<div class="line"><a name="l00708"></a><span class="lineno">  708</span>&#160;  };</div>
<div class="line"><a name="l00709"></a><span class="lineno">  709</span>&#160; </div>
<div class="line"><a name="l00710"></a><span class="lineno">  710</span>&#160;  <span class="keyword">template</span>&lt;<span class="keyword">typename</span> Dest&gt; <span class="keywordtype">void</span> evalTo(Dest&amp; dst)<span class="keyword"> const</span></div>
<div class="line"><a name="l00711"></a><span class="lineno">  711</span>&#160;<span class="keyword">  </span>{</div>
<div class="line"><a name="l00712"></a><span class="lineno">  712</span>&#160;    <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00713"></a><span class="lineno">  713</span>&#160;    <span class="keywordflow">if</span>(rank() == 0)</div>
<div class="line"><a name="l00714"></a><span class="lineno">  714</span>&#160;    {</div>
<div class="line"><a name="l00715"></a><span class="lineno">  715</span>&#160;      <span class="comment">// The Image is just {0}, so it doesn&#39;t have a basis properly speaking, but let&#39;s</span></div>
<div class="line"><a name="l00716"></a><span class="lineno">  716</span>&#160;      <span class="comment">// avoid crashing/asserting as that depends on floating point calculations. Let&#39;s</span></div>
<div class="line"><a name="l00717"></a><span class="lineno">  717</span>&#160;      <span class="comment">// just return a single column vector filled with zeros.</span></div>
<div class="line"><a name="l00718"></a><span class="lineno">  718</span>&#160;      dst.setZero();</div>
<div class="line"><a name="l00719"></a><span class="lineno">  719</span>&#160;      <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00720"></a><span class="lineno">  720</span>&#160;    }</div>
<div class="line"><a name="l00721"></a><span class="lineno">  721</span>&#160; </div>
<div class="line"><a name="l00722"></a><span class="lineno">  722</span>&#160;    Matrix&lt;Index, Dynamic, 1, 0, MaxSmallDimAtCompileTime, 1&gt; pivots(rank());</div>
<div class="line"><a name="l00723"></a><span class="lineno">  723</span>&#160;    RealScalar premultiplied_threshold = dec().maxPivot() * dec().threshold();</div>
<div class="line"><a name="l00724"></a><span class="lineno">  724</span>&#160;    <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> p = 0;</div>
<div class="line"><a name="l00725"></a><span class="lineno">  725</span>&#160;    <span class="keywordflow">for</span>(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = 0; i &lt; dec().nonzeroPivots(); ++i)</div>
<div class="line"><a name="l00726"></a><span class="lineno">  726</span>&#160;      <span class="keywordflow">if</span>(<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(dec().matrixLU().coeff(i,i)) &gt; premultiplied_threshold)</div>
<div class="line"><a name="l00727"></a><span class="lineno">  727</span>&#160;        pivots.coeffRef(p++) = i;</div>
<div class="line"><a name="l00728"></a><span class="lineno">  728</span>&#160;    eigen_internal_assert(p == rank());</div>
<div class="line"><a name="l00729"></a><span class="lineno">  729</span>&#160; </div>
<div class="line"><a name="l00730"></a><span class="lineno">  730</span>&#160;    <span class="keywordflow">for</span>(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = 0; i &lt; rank(); ++i)</div>
<div class="line"><a name="l00731"></a><span class="lineno">  731</span>&#160;      dst.col(i) = originalMatrix().col(dec().permutationQ().indices().coeff(pivots.coeff(i)));</div>
<div class="line"><a name="l00732"></a><span class="lineno">  732</span>&#160;  }</div>
<div class="line"><a name="l00733"></a><span class="lineno">  733</span>&#160;};</div>
<div class="line"><a name="l00734"></a><span class="lineno">  734</span>&#160; </div>
<div class="line"><a name="l00735"></a><span class="lineno">  735</span>&#160;<span class="comment">/***** Implementation of solve() *****************************************************/</span></div>
<div class="line"><a name="l00736"></a><span class="lineno">  736</span>&#160; </div>
<div class="line"><a name="l00737"></a><span class="lineno">  737</span>&#160;} <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00738"></a><span class="lineno">  738</span>&#160; </div>
<div class="line"><a name="l00739"></a><span class="lineno">  739</span>&#160;<span class="preprocessor">#ifndef EIGEN_PARSED_BY_DOXYGEN</span></div>
<div class="line"><a name="l00740"></a><span class="lineno">  740</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType_&gt;</div>
<div class="line"><a name="l00741"></a><span class="lineno">  741</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> RhsType, <span class="keyword">typename</span> DstType&gt;</div>
<div class="line"><a name="l00742"></a><span class="lineno">  742</span>&#160;<span class="keywordtype">void</span> FullPivLU&lt;MatrixType_&gt;::_solve_impl(<span class="keyword">const</span> RhsType &amp;rhs, DstType &amp;dst)<span class="keyword"> const</span></div>
<div class="line"><a name="l00743"></a><span class="lineno">  743</span>&#160;<span class="keyword"></span>{</div>
<div class="line"><a name="l00744"></a><span class="lineno">  744</span>&#160;  <span class="comment">/* The decomposition PAQ = LU can be rewritten as A = P^{-1} L U Q^{-1}.</span></div>
<div class="line"><a name="l00745"></a><span class="lineno">  745</span>&#160;<span class="comment">  * So we proceed as follows:</span></div>
<div class="line"><a name="l00746"></a><span class="lineno">  746</span>&#160;<span class="comment">  * Step 1: compute c = P * rhs.</span></div>
<div class="line"><a name="l00747"></a><span class="lineno">  747</span>&#160;<span class="comment">  * Step 2: replace c by the solution x to Lx = c. Exists because L is invertible.</span></div>
<div class="line"><a name="l00748"></a><span class="lineno">  748</span>&#160;<span class="comment">  * Step 3: replace c by the solution x to Ux = c. May or may not exist.</span></div>
<div class="line"><a name="l00749"></a><span class="lineno">  749</span>&#160;<span class="comment">  * Step 4: result = Q * c;</span></div>
<div class="line"><a name="l00750"></a><span class="lineno">  750</span>&#160;<span class="comment">  */</span></div>
<div class="line"><a name="l00751"></a><span class="lineno">  751</span>&#160; </div>
<div class="line"><a name="l00752"></a><span class="lineno">  752</span>&#160;  <span class="keyword">const</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> rows = this-&gt;rows(),</div>
<div class="line"><a name="l00753"></a><span class="lineno">  753</span>&#160;              cols = this-&gt;cols(),</div>
<div class="line"><a name="l00754"></a><span class="lineno">  754</span>&#160;              nonzero_pivots = this-&gt;rank();</div>
<div class="line"><a name="l00755"></a><span class="lineno">  755</span>&#160;  <span class="keyword">const</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> smalldim = (std::min)(rows, cols);</div>
<div class="line"><a name="l00756"></a><span class="lineno">  756</span>&#160; </div>
<div class="line"><a name="l00757"></a><span class="lineno">  757</span>&#160;  <span class="keywordflow">if</span>(nonzero_pivots == 0)</div>
<div class="line"><a name="l00758"></a><span class="lineno">  758</span>&#160;  {</div>
<div class="line"><a name="l00759"></a><span class="lineno">  759</span>&#160;    dst.setZero();</div>
<div class="line"><a name="l00760"></a><span class="lineno">  760</span>&#160;    <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00761"></a><span class="lineno">  761</span>&#160;  }</div>
<div class="line"><a name="l00762"></a><span class="lineno">  762</span>&#160; </div>
<div class="line"><a name="l00763"></a><span class="lineno">  763</span>&#160;  <span class="keyword">typename</span> RhsType::PlainObject c(rhs.rows(), rhs.cols());</div>
<div class="line"><a name="l00764"></a><span class="lineno">  764</span>&#160; </div>
<div class="line"><a name="l00765"></a><span class="lineno">  765</span>&#160;  <span class="comment">// Step 1</span></div>
<div class="line"><a name="l00766"></a><span class="lineno">  766</span>&#160;  c = permutationP() * rhs;</div>
<div class="line"><a name="l00767"></a><span class="lineno">  767</span>&#160; </div>
<div class="line"><a name="l00768"></a><span class="lineno">  768</span>&#160;  <span class="comment">// Step 2</span></div>
<div class="line"><a name="l00769"></a><span class="lineno">  769</span>&#160;  m_lu.topLeftCorner(smalldim,smalldim)</div>
<div class="line"><a name="l00770"></a><span class="lineno">  770</span>&#160;      .template triangularView&lt;UnitLower&gt;()</div>
<div class="line"><a name="l00771"></a><span class="lineno">  771</span>&#160;      .solveInPlace(c.topRows(smalldim));</div>
<div class="line"><a name="l00772"></a><span class="lineno">  772</span>&#160;  <span class="keywordflow">if</span>(rows&gt;cols)</div>
<div class="line"><a name="l00773"></a><span class="lineno">  773</span>&#160;    c.bottomRows(rows-cols) -= m_lu.bottomRows(rows-cols) * c.topRows(cols);</div>
<div class="line"><a name="l00774"></a><span class="lineno">  774</span>&#160; </div>
<div class="line"><a name="l00775"></a><span class="lineno">  775</span>&#160;  <span class="comment">// Step 3</span></div>
<div class="line"><a name="l00776"></a><span class="lineno">  776</span>&#160;  m_lu.topLeftCorner(nonzero_pivots, nonzero_pivots)</div>
<div class="line"><a name="l00777"></a><span class="lineno">  777</span>&#160;      .template triangularView&lt;Upper&gt;()</div>
<div class="line"><a name="l00778"></a><span class="lineno">  778</span>&#160;      .solveInPlace(c.topRows(nonzero_pivots));</div>
<div class="line"><a name="l00779"></a><span class="lineno">  779</span>&#160; </div>
<div class="line"><a name="l00780"></a><span class="lineno">  780</span>&#160;  <span class="comment">// Step 4</span></div>
<div class="line"><a name="l00781"></a><span class="lineno">  781</span>&#160;  <span class="keywordflow">for</span>(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = 0; i &lt; nonzero_pivots; ++i)</div>
<div class="line"><a name="l00782"></a><span class="lineno">  782</span>&#160;    dst.row(permutationQ().indices().coeff(i)) = c.row(i);</div>
<div class="line"><a name="l00783"></a><span class="lineno">  783</span>&#160;  <span class="keywordflow">for</span>(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = nonzero_pivots; i &lt; m_lu.cols(); ++i)</div>
<div class="line"><a name="l00784"></a><span class="lineno">  784</span>&#160;    dst.row(permutationQ().indices().coeff(i)).setZero();</div>
<div class="line"><a name="l00785"></a><span class="lineno">  785</span>&#160;}</div>
<div class="line"><a name="l00786"></a><span class="lineno">  786</span>&#160; </div>
<div class="line"><a name="l00787"></a><span class="lineno">  787</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType_&gt;</div>
<div class="line"><a name="l00788"></a><span class="lineno">  788</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">bool</span> Conjugate, <span class="keyword">typename</span> RhsType, <span class="keyword">typename</span> DstType&gt;</div>
<div class="line"><a name="l00789"></a><span class="lineno">  789</span>&#160;<span class="keywordtype">void</span> FullPivLU&lt;MatrixType_&gt;::_solve_impl_transposed(<span class="keyword">const</span> RhsType &amp;rhs, DstType &amp;dst)<span class="keyword"> const</span></div>
<div class="line"><a name="l00790"></a><span class="lineno">  790</span>&#160;<span class="keyword"></span>{</div>
<div class="line"><a name="l00791"></a><span class="lineno">  791</span>&#160;  <span class="comment">/* The decomposition PAQ = LU can be rewritten as A = P^{-1} L U Q^{-1},</span></div>
<div class="line"><a name="l00792"></a><span class="lineno">  792</span>&#160;<span class="comment">   * and since permutations are real and unitary, we can write this</span></div>
<div class="line"><a name="l00793"></a><span class="lineno">  793</span>&#160;<span class="comment">   * as   A^T = Q U^T L^T P,</span></div>
<div class="line"><a name="l00794"></a><span class="lineno">  794</span>&#160;<span class="comment">   * So we proceed as follows:</span></div>
<div class="line"><a name="l00795"></a><span class="lineno">  795</span>&#160;<span class="comment">   * Step 1: compute c = Q^T rhs.</span></div>
<div class="line"><a name="l00796"></a><span class="lineno">  796</span>&#160;<span class="comment">   * Step 2: replace c by the solution x to U^T x = c. May or may not exist.</span></div>
<div class="line"><a name="l00797"></a><span class="lineno">  797</span>&#160;<span class="comment">   * Step 3: replace c by the solution x to L^T x = c.</span></div>
<div class="line"><a name="l00798"></a><span class="lineno">  798</span>&#160;<span class="comment">   * Step 4: result = P^T c.</span></div>
<div class="line"><a name="l00799"></a><span class="lineno">  799</span>&#160;<span class="comment">   * If Conjugate is true, replace &quot;^T&quot; by &quot;^*&quot; above.</span></div>
<div class="line"><a name="l00800"></a><span class="lineno">  800</span>&#160;<span class="comment">   */</span></div>
<div class="line"><a name="l00801"></a><span class="lineno">  801</span>&#160; </div>
<div class="line"><a name="l00802"></a><span class="lineno">  802</span>&#160;  <span class="keyword">const</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> rows = this-&gt;rows(), cols = this-&gt;cols(),</div>
<div class="line"><a name="l00803"></a><span class="lineno">  803</span>&#160;    nonzero_pivots = this-&gt;rank();</div>
<div class="line"><a name="l00804"></a><span class="lineno">  804</span>&#160;  <span class="keyword">const</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> smalldim = (std::min)(rows, cols);</div>
<div class="line"><a name="l00805"></a><span class="lineno">  805</span>&#160; </div>
<div class="line"><a name="l00806"></a><span class="lineno">  806</span>&#160;  <span class="keywordflow">if</span>(nonzero_pivots == 0)</div>
<div class="line"><a name="l00807"></a><span class="lineno">  807</span>&#160;  {</div>
<div class="line"><a name="l00808"></a><span class="lineno">  808</span>&#160;    dst.setZero();</div>
<div class="line"><a name="l00809"></a><span class="lineno">  809</span>&#160;    <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00810"></a><span class="lineno">  810</span>&#160;  }</div>
<div class="line"><a name="l00811"></a><span class="lineno">  811</span>&#160; </div>
<div class="line"><a name="l00812"></a><span class="lineno">  812</span>&#160;  <span class="keyword">typename</span> RhsType::PlainObject c(rhs.rows(), rhs.cols());</div>
<div class="line"><a name="l00813"></a><span class="lineno">  813</span>&#160; </div>
<div class="line"><a name="l00814"></a><span class="lineno">  814</span>&#160;  <span class="comment">// Step 1</span></div>
<div class="line"><a name="l00815"></a><span class="lineno">  815</span>&#160;  c = permutationQ().inverse() * rhs;</div>
<div class="line"><a name="l00816"></a><span class="lineno">  816</span>&#160; </div>
<div class="line"><a name="l00817"></a><span class="lineno">  817</span>&#160;  <span class="comment">// Step 2</span></div>
<div class="line"><a name="l00818"></a><span class="lineno">  818</span>&#160;  m_lu.topLeftCorner(nonzero_pivots, nonzero_pivots)</div>
<div class="line"><a name="l00819"></a><span class="lineno">  819</span>&#160;      .template triangularView&lt;Upper&gt;()</div>
<div class="line"><a name="l00820"></a><span class="lineno">  820</span>&#160;      .transpose()</div>
<div class="line"><a name="l00821"></a><span class="lineno">  821</span>&#160;      .template conjugateIf&lt;Conjugate&gt;()</div>
<div class="line"><a name="l00822"></a><span class="lineno">  822</span>&#160;      .solveInPlace(c.topRows(nonzero_pivots));</div>
<div class="line"><a name="l00823"></a><span class="lineno">  823</span>&#160; </div>
<div class="line"><a name="l00824"></a><span class="lineno">  824</span>&#160;  <span class="comment">// Step 3</span></div>
<div class="line"><a name="l00825"></a><span class="lineno">  825</span>&#160;  m_lu.topLeftCorner(smalldim, smalldim)</div>
<div class="line"><a name="l00826"></a><span class="lineno">  826</span>&#160;      .template triangularView&lt;UnitLower&gt;()</div>
<div class="line"><a name="l00827"></a><span class="lineno">  827</span>&#160;      .transpose()</div>
<div class="line"><a name="l00828"></a><span class="lineno">  828</span>&#160;      .template conjugateIf&lt;Conjugate&gt;()</div>
<div class="line"><a name="l00829"></a><span class="lineno">  829</span>&#160;      .solveInPlace(c.topRows(smalldim));</div>
<div class="line"><a name="l00830"></a><span class="lineno">  830</span>&#160; </div>
<div class="line"><a name="l00831"></a><span class="lineno">  831</span>&#160;  <span class="comment">// Step 4</span></div>
<div class="line"><a name="l00832"></a><span class="lineno">  832</span>&#160;  PermutationPType invp = permutationP().inverse().eval();</div>
<div class="line"><a name="l00833"></a><span class="lineno">  833</span>&#160;  <span class="keywordflow">for</span>(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = 0; i &lt; smalldim; ++i)</div>
<div class="line"><a name="l00834"></a><span class="lineno">  834</span>&#160;    dst.row(invp.indices().coeff(i)) = c.row(i);</div>
<div class="line"><a name="l00835"></a><span class="lineno">  835</span>&#160;  <span class="keywordflow">for</span>(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = smalldim; i &lt; rows; ++i)</div>
<div class="line"><a name="l00836"></a><span class="lineno">  836</span>&#160;    dst.row(invp.indices().coeff(i)).setZero();</div>
<div class="line"><a name="l00837"></a><span class="lineno">  837</span>&#160;}</div>
<div class="line"><a name="l00838"></a><span class="lineno">  838</span>&#160; </div>
<div class="line"><a name="l00839"></a><span class="lineno">  839</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00840"></a><span class="lineno">  840</span>&#160; </div>
<div class="line"><a name="l00841"></a><span class="lineno">  841</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00842"></a><span class="lineno">  842</span>&#160; </div>
<div class="line"><a name="l00843"></a><span class="lineno">  843</span>&#160; </div>
<div class="line"><a name="l00844"></a><span class="lineno">  844</span>&#160;<span class="comment">/***** Implementation of inverse() *****************************************************/</span></div>
<div class="line"><a name="l00845"></a><span class="lineno">  845</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> DstXprType, <span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00846"></a><span class="lineno">  846</span>&#160;<span class="keyword">struct </span>Assignment&lt;DstXprType, Inverse&lt;FullPivLU&lt;MatrixType&gt; &gt;, internal::assign_op&lt;typename DstXprType::Scalar,typename FullPivLU&lt;MatrixType&gt;::Scalar&gt;, Dense2Dense&gt;</div>
<div class="line"><a name="l00847"></a><span class="lineno">  847</span>&#160;{</div>
<div class="line"><a name="l00848"></a><span class="lineno">  848</span>&#160;  <span class="keyword">typedef</span> FullPivLU&lt;MatrixType&gt; LuType;</div>
<div class="line"><a name="l00849"></a><span class="lineno">  849</span>&#160;  <span class="keyword">typedef</span> Inverse&lt;LuType&gt; SrcXprType;</div>
<div class="line"><a name="l00850"></a><span class="lineno">  850</span>&#160;  <span class="keyword">static</span> <span class="keywordtype">void</span> run(DstXprType &amp;dst, <span class="keyword">const</span> SrcXprType &amp;src, <span class="keyword">const</span> internal::assign_op&lt;typename DstXprType::Scalar,typename MatrixType::Scalar&gt; &amp;)</div>
<div class="line"><a name="l00851"></a><span class="lineno">  851</span>&#160;  {</div>
<div class="line"><a name="l00852"></a><span class="lineno">  852</span>&#160;    dst = src.nestedExpression().<a class="code" href="classEigen_1_1SolverBase.html#a7fd647d110487799205df6f99547879d">solve</a>(MatrixType::Identity(src.rows(), src.cols()));</div>
<div class="line"><a name="l00853"></a><span class="lineno">  853</span>&#160;  }</div>
<div class="line"><a name="l00854"></a><span class="lineno">  854</span>&#160;};</div>
<div class="line"><a name="l00855"></a><span class="lineno">  855</span>&#160;} <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00856"></a><span class="lineno">  856</span>&#160; </div>
<div class="line"><a name="l00857"></a><span class="lineno">  857</span>&#160;<span class="comment">/******* MatrixBase methods *****************************************************************/</span></div>
<div class="line"><a name="l00858"></a><span class="lineno">  858</span>&#160; </div>
<div class="line"><a name="l00865"></a><span class="lineno">  865</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> Derived&gt;</div>
<div class="line"><a name="l00866"></a><span class="lineno">  866</span>&#160;<span class="keyword">inline</span> <span class="keyword">const</span> FullPivLU&lt;typename MatrixBase&lt;Derived&gt;::PlainObject&gt;</div>
<div class="line"><a name="l00867"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a25da97d31acab0ee5d9d13bdbb0569da">  867</a></span>&#160;<a class="code" href="classEigen_1_1MatrixBase.html#a25da97d31acab0ee5d9d13bdbb0569da">MatrixBase&lt;Derived&gt;::fullPivLu</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00868"></a><span class="lineno">  868</span>&#160;<span class="keyword"></span>{</div>
<div class="line"><a name="l00869"></a><span class="lineno">  869</span>&#160;  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1FullPivLU.html">FullPivLU&lt;PlainObject&gt;</a>(eval());</div>
<div class="line"><a name="l00870"></a><span class="lineno">  870</span>&#160;}</div>
<div class="line"><a name="l00871"></a><span class="lineno">  871</span>&#160; </div>
<div class="line"><a name="l00872"></a><span class="lineno">  872</span>&#160;} <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00873"></a><span class="lineno">  873</span>&#160; </div>
<div class="line"><a name="l00874"></a><span class="lineno">  874</span>&#160;<span class="preprocessor">#endif </span><span class="comment">// EIGEN_LU_H</span></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html"><div class="ttname"><a href="classEigen_1_1FullPivLU.html">Eigen::FullPivLU</a></div><div class="ttdoc">LU decomposition of a matrix with complete pivoting, and related features.</div><div class="ttdef"><b>Definition:</b> FullPivLU.h:64</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_a05cedf8dca6394355ef64c1ea1374b4a"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#a05cedf8dca6394355ef64c1ea1374b4a">Eigen::FullPivLU::maxPivot</a></div><div class="ttdeci">RealScalar maxPivot() const</div><div class="ttdef"><b>Definition:</b> FullPivLU.h:156</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_a0ee7753645eb31bcbd5faa459168b294"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#a0ee7753645eb31bcbd5faa459168b294">Eigen::FullPivLU::isInvertible</a></div><div class="ttdeci">bool isInvertible() const</div><div class="ttdef"><b>Definition:</b> FullPivLU.h:387</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_a191a4f598b0c192a83ab48984e87ee51"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#a191a4f598b0c192a83ab48984e87ee51">Eigen::FullPivLU::reconstructedMatrix</a></div><div class="ttdeci">MatrixType reconstructedMatrix() const</div><div class="ttdef"><b>Definition:</b> FullPivLU.h:589</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_a25b70ffbc88d804981c8874da55e7419"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#a25b70ffbc88d804981c8874da55e7419">Eigen::FullPivLU::permutationQ</a></div><div class="ttdeci">const PermutationQType &amp; permutationQ() const</div><div class="ttdef"><b>Definition:</b> FullPivLU.h:172</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_a34afc848d7fb22c7a56a053d3807d2cd"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#a34afc848d7fb22c7a56a053d3807d2cd">Eigen::FullPivLU::inverse</a></div><div class="ttdeci">const Inverse&lt; FullPivLU &gt; inverse() const</div><div class="ttdef"><b>Definition:</b> FullPivLU.h:400</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_a358cec49914ec3cd3707e6b79ae32d0b"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#a358cec49914ec3cd3707e6b79ae32d0b">Eigen::FullPivLU::dimensionOfKernel</a></div><div class="ttdeci">Index dimensionOfKernel() const</div><div class="ttdef"><b>Definition:</b> FullPivLU.h:349</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_a396f63d737e0613f41004e30be8fe3cf"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#a396f63d737e0613f41004e30be8fe3cf">Eigen::FullPivLU::compute</a></div><div class="ttdeci">FullPivLU &amp; compute(const EigenBase&lt; InputType &gt; &amp;matrix)</div><div class="ttdef"><b>Definition:</b> FullPivLU.h:122</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_a3e7d7a53f5b7c4ba99013fe171ac5654"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#a3e7d7a53f5b7c4ba99013fe171ac5654">Eigen::FullPivLU::matrixLU</a></div><div class="ttdeci">const MatrixType &amp; matrixLU() const</div><div class="ttdef"><b>Definition:</b> FullPivLU.h:134</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_a3eb3aa0c37e06ffaf0c07b1eeb0995cc"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#a3eb3aa0c37e06ffaf0c07b1eeb0995cc">Eigen::FullPivLU::permutationP</a></div><div class="ttdeci">const PermutationPType &amp; permutationP() const</div><div class="ttdef"><b>Definition:</b> FullPivLU.h:162</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_a614d3aa28e6af7b2af8630d3e2d022d8"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#a614d3aa28e6af7b2af8630d3e2d022d8">Eigen::FullPivLU::solve</a></div><div class="ttdeci">const Solve&lt; FullPivLU, Rhs &gt; solve(const MatrixBase&lt; Rhs &gt; &amp;b) const</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_a71654e5c60a26407ecccfaa5b34bb0aa"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#a71654e5c60a26407ecccfaa5b34bb0aa">Eigen::FullPivLU::determinant</a></div><div class="ttdeci">internal::traits&lt; MatrixType &gt;::Scalar determinant() const</div><div class="ttdef"><b>Definition:</b> FullPivLU.h:578</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_a8d31c78a17a70d56ef2d105d6b5efec3"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#a8d31c78a17a70d56ef2d105d6b5efec3">Eigen::FullPivLU::rank</a></div><div class="ttdeci">Index rank() const</div><div class="ttdef"><b>Definition:</b> FullPivLU.h:332</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_a90dd33c632ba890175f61eac054bde98"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#a90dd33c632ba890175f61eac054bde98">Eigen::FullPivLU::isInjective</a></div><div class="ttdeci">bool isInjective() const</div><div class="ttdef"><b>Definition:</b> FullPivLU.h:362</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_aa8cbf984141608e89b503125690d24d4"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#aa8cbf984141608e89b503125690d24d4">Eigen::FullPivLU::image</a></div><div class="ttdeci">const internal::image_retval&lt; FullPivLU &gt; image(const MatrixType &amp;originalMatrix) const</div><div class="ttdef"><b>Definition:</b> FullPivLU.h:218</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_aad90c46ea08618ae485fce4e5f4677d0"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#aad90c46ea08618ae485fce4e5f4677d0">Eigen::FullPivLU::nonzeroPivots</a></div><div class="ttdeci">Index nonzeroPivots() const</div><div class="ttdef"><b>Definition:</b> FullPivLU.h:147</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_abad257b6db0856d8ec52c6072f58f75d"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#abad257b6db0856d8ec52c6072f58f75d">Eigen::FullPivLU::setThreshold</a></div><div class="ttdeci">FullPivLU &amp; setThreshold(const RealScalar &amp;threshold)</div><div class="ttdef"><b>Definition:</b> FullPivLU.h:292</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_adfc1e27ff60287be5313b5efc3559308"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#adfc1e27ff60287be5313b5efc3559308">Eigen::FullPivLU::kernel</a></div><div class="ttdeci">const internal::kernel_retval&lt; FullPivLU &gt; kernel() const</div><div class="ttdef"><b>Definition:</b> FullPivLU.h:192</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_ae2298a7a89749dee7d86f02ccacce0cb"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#ae2298a7a89749dee7d86f02ccacce0cb">Eigen::FullPivLU::threshold</a></div><div class="ttdeci">RealScalar threshold() const</div><div class="ttdef"><b>Definition:</b> FullPivLU.h:317</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_ae39fcfa8d1319472a5b2adfa7a28d9cf"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#ae39fcfa8d1319472a5b2adfa7a28d9cf">Eigen::FullPivLU::rcond</a></div><div class="ttdeci">RealScalar rcond() const</div><div class="ttdef"><b>Definition:</b> FullPivLU.h:252</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_aeafbb0b885cc4c28b53e77988ac5cfe3"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#aeafbb0b885cc4c28b53e77988ac5cfe3">Eigen::FullPivLU::setThreshold</a></div><div class="ttdeci">FullPivLU &amp; setThreshold(Default_t)</div><div class="ttdef"><b>Definition:</b> FullPivLU.h:307</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_af225528d1c6e623a2b1dce091907d13e"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#af225528d1c6e623a2b1dce091907d13e">Eigen::FullPivLU::FullPivLU</a></div><div class="ttdeci">FullPivLU()</div><div class="ttdoc">Default Constructor.</div><div class="ttdef"><b>Definition:</b> FullPivLU.h:441</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_af42b9cb6356658b92b2d1006aee73fc4"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#af42b9cb6356658b92b2d1006aee73fc4">Eigen::FullPivLU::isSurjective</a></div><div class="ttdeci">bool isSurjective() const</div><div class="ttdef"><b>Definition:</b> FullPivLU.h:375</div></div>
<div class="ttc" id="aclassEigen_1_1Inverse_html"><div class="ttname"><a href="classEigen_1_1Inverse.html">Eigen::Inverse</a></div><div class="ttdoc">Expression of the inverse of another expression.</div><div class="ttdef"><b>Definition:</b> Inverse.h:46</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixBase_html"><div class="ttname"><a href="classEigen_1_1MatrixBase.html">Eigen::MatrixBase</a></div><div class="ttdoc">Base class for all dense matrices, vectors, and expressions.</div><div class="ttdef"><b>Definition:</b> MatrixBase.h:52</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixBase_html_a25da97d31acab0ee5d9d13bdbb0569da"><div class="ttname"><a href="classEigen_1_1MatrixBase.html#a25da97d31acab0ee5d9d13bdbb0569da">Eigen::MatrixBase::fullPivLu</a></div><div class="ttdeci">const FullPivLU&lt; PlainObject &gt; fullPivLu() const</div><div class="ttdef"><b>Definition:</b> FullPivLU.h:867</div></div>
<div class="ttc" id="aclassEigen_1_1PermutationMatrix_html"><div class="ttname"><a href="classEigen_1_1PermutationMatrix.html">Eigen::PermutationMatrix&lt; ColsAtCompileTime, MaxColsAtCompileTime &gt;</a></div></div>
<div class="ttc" id="aclassEigen_1_1Solve_html"><div class="ttname"><a href="classEigen_1_1Solve.html">Eigen::Solve</a></div><div class="ttdoc">Pseudo expression representing a solving operation.</div><div class="ttdef"><b>Definition:</b> Solve.h:65</div></div>
<div class="ttc" id="aclassEigen_1_1SolverBase_html"><div class="ttname"><a href="classEigen_1_1SolverBase.html">Eigen::SolverBase</a></div><div class="ttdoc">A base class for matrix decomposition and solvers.</div><div class="ttdef"><b>Definition:</b> SolverBase.h:71</div></div>
<div class="ttc" id="aclassEigen_1_1SolverBase_html_a7fd647d110487799205df6f99547879d"><div class="ttname"><a href="classEigen_1_1SolverBase.html#a7fd647d110487799205df6f99547879d">Eigen::SolverBase::solve</a></div><div class="ttdeci">const Solve&lt; Derived, Rhs &gt; solve(const MatrixBase&lt; Rhs &gt; &amp;b) const</div><div class="ttdef"><b>Definition:</b> SolverBase.h:107</div></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div><div class="ttdef"><b>Definition:</b> Core:139</div></div>
<div class="ttc" id="anamespaceEigen_html_a62e77e0933482dafde8fe197d9a2cfde"><div class="ttname"><a href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a></div><div class="ttdeci">EIGEN_DEFAULT_DENSE_INDEX_TYPE Index</div><div class="ttdoc">The Index type as used for the API.</div><div class="ttdef"><b>Definition:</b> Meta.h:59</div></div>
<div class="ttc" id="anamespaceEigen_html_ad81fa7195215a0ce30017dfac309f0b2"><div class="ttname"><a href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Eigen::Dynamic</a></div><div class="ttdeci">const int Dynamic</div><div class="ttdef"><b>Definition:</b> Constants.h:24</div></div>
<div class="ttc" id="anamespaceEigen_html_ae27242789e7e62a8c42579b79be59b1a"><div class="ttname"><a href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">Eigen::abs</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_abs_op&lt; typename Derived::Scalar &gt;, const Derived &gt; abs(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="astructEigen_1_1EigenBase_html"><div class="ttname"><a href="structEigen_1_1EigenBase.html">Eigen::EigenBase</a></div><div class="ttdef"><b>Definition:</b> EigenBase.h:32</div></div>
<div class="ttc" id="astructEigen_1_1EigenBase_html_a1fbabe7f12bcbfba3b9a448b1f5e46fa"><div class="ttname"><a href="structEigen_1_1EigenBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">Eigen::EigenBase::derived</a></div><div class="ttdeci">Derived &amp; derived()</div><div class="ttdef"><b>Definition:</b> EigenBase.h:48</div></div>
<div class="ttc" id="astructEigen_1_1EigenBase_html_a554f30542cc2316add4b1ea0a492ff02"><div class="ttname"><a href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Eigen::EigenBase::Index</a></div><div class="ttdeci">Eigen::Index Index</div><div class="ttdoc">The interface type of indices.</div><div class="ttdef"><b>Definition:</b> EigenBase.h:41</div></div>
<div class="ttc" id="astructEigen_1_1NumTraits_html"><div class="ttname"><a href="structEigen_1_1NumTraits.html">Eigen::NumTraits</a></div><div class="ttdoc">Holds information about the various numeric (i.e. scalar) types allowed by Eigen.</div><div class="ttdef"><b>Definition:</b> NumTraits.h:231</div></div>
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